Simulation Based Engineering in Fluid Flow Design (eBook)

Professor J.S. Rao is Chief Science office at Altair Engineering India Ltd, President of the Vibration Institute of India and Editor in chief of the Journal of Vibration Engineering and Technologies.

Preface 6
Acknowledgments 9
Contents 11
1 Introduction 14
Abstract 14
2 Fluid Statics 36
Abstract 36
2.1 States of Matter 36
2.2 Pressure in Fluids at Rest 37
2.3 Buoyancy 42
2.3.1 Application of Buoyancy Principle to the Stability of a Ship 44
2.3.2 Balloons and Airships 45
2.3.3 Hydrostatics of Dam 46
2.4 Basics of Thermodynamics 49
2.4.1 Zeroth Law 50
2.4.2 Hydrostatics of Gases 50
2.4.3 Vapor Pressure 51
2.4.4 Internal Energy 53
2.4.5 Enthalpy 53
2.4.6 Specific Heats 54
2.4.7 Polytropic Form for Pressure-Specific Volume Relation 55
2.4.8 First Law of Thermodynamics 57
2.4.9 Adiabatic Process 58
2.4.10 Irreversible Process 58
2.4.11 Reversible Process 59
2.4.12 Entropy and Second Law of Thermodynamics 59
2.4.13 Entropy 60
2.4.14 Entropy Calculation for Any Process 61
2.4.15 Isentropic Process 62
3 Fluid Dynamics 67
Abstract 67
3.1 Characteristics of Fluids 70
3.2 Mass Balance 72
3.3 Force Balance and Momentum Equations 74
3.4 Energy Equation 77
3.5 Kinetic Energy 81
3.6 Internal Energy 81
3.7 Shear Stresses 82
3.8 Equations of Motion 83
3.9 Summary of Fluid Flow Equations 84
4 Finite Volume Method—Diffusion Problems 86
Abstract 86
4.1 Diffusion Problem 88
4.2 Diffusion with Source Term 95
4.3 Diffusion with Convection 101
5 Finite Volume Method—Convection-Diffusion Problems 110
Abstract 110
5.1 Steady State One-Dimensional Convection and Diffusion 110
5.1.1 Exact Solution for Convection-Diffusion Problem 113
5.1.2 Finite Volume Method for Convection-Diffusion Problem 114
6 Pressure—Velocity Coupling in Steady Flows 117
Abstract 117
6.1 Steady State One-Dimensional Incompressible Problem 118
6.1.1 Streamline Flow 119
6.2 Pitot and Venturi Tubes 121
6.3 Stagnation Conditions in Adiabatic Flow 124
6.4 Isentropic Flow 125
6.5 Speed of Sound 126
6.6 Shocks in Supersonic Flow 129
6.7 Other Forms of Energy Equation for Adiabatic Flow 131
6.7.1 Mach Number for Which the Flow Can Be Considered Incompressible 133
6.7.2 Characteristic Mach Number 135
6.8 Quasi-One Dimensional Flow 135
6.9 Area-Velocity Relation 138
6.9.1 Continuity Equation in Differential Form 138
6.9.2 Momentum Equation in Differential Form 139
6.9.3 Energy Equation in Differential Form 140
6.10 Example of Nozzle Flow—Subsonic Flow Throughout 142
6.10.1 Example of Axisymmetric Nozzle Flow 144
6.10.2 Subsonic Flow 147
6.11 Nozzle Flow—Subsonic Flow with Sonic Conditions at the Throat 150
6.12 Nozzle Flow—Supersonic Flow with Perfect Expansion 152
6.13 CFD Solution of Isentropic Flow in Converging-Diverging Nozzles 154
7 Turbulence 164
Abstract 164
7.1 What Is Turbulence? 166
7.2 Reynolds Equations 168
7.2.1 Reynolds Averaged Navier-Stokes Equations, RANS 170
7.2.2 Boussinesq Hypothesis 171
7.2.3 Prandtl’s Mixing Length Model 172
7.2.4 k-? Model 172
7.3 Nozzle Flow with a Normal Shock in the Divergent Portion 175
7.3.1 Normal Shock 175
7.4 CFD Solution of Flow in Converging-Diverging Nozzles with a Normal Shock 184
8 Epilogue 188
Abstract 188
Acknowledgments 189
Index 190